GATE CSE
First time here? Checkout the FAQ!
x
0 votes
77 views

Which of the following is/are true ?

  • A. $\text{R}$ is a reflexive relation on a set $\text{A}$, then $\text{R}^{n}$ is reflexive for all $n\geq0$
  • B. Relation $\text{R}$ on set $A$ is reflexive if and only if inverse relation $R^{-1}$ is reflexive.
  • C  Relation $\text{R}$ on set $A$ is antisymmetric if and only $R \cap R^{-1}$   is a subest of diagonal relation $\Delta = \left \{ (a,a) \; | a \in A \right \}$
  • D. $M_{S\circ R} = M_R \; \odot M_S$ where $\odot$ is boolean product.
asked in Set Theory & Algebra by Veteran (45.6k points)  
edited by | 77 views
All seems true.

C. Let M be a adjacency matrix for R & M' be for $R^{-1}$ . M & M' are mutually transpose of each other, but diagonal remains same for both. Therefore $R\cap{R^{-1}}$ is nothing but $2^{n}$ numbers of diagonal fills of adjacency matrix which is sign of anti symmetric relations.

Let me know where I'm wrong if I'm.

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.


Top Users Apr 2017
  1. akash.dinkar12

    3660 Points

  2. Divya Bharti

    2580 Points

  3. Deepthi_ts

    2040 Points

  4. rude

    1966 Points

  5. Tesla!

    1768 Points

  6. Debashish Deka

    1614 Points

  7. Shubham Sharma 2

    1610 Points

  8. Prashant.

    1492 Points

  9. Arjun

    1472 Points

  10. Arunav Khare

    1464 Points

Monthly Topper: Rs. 500 gift card

22,088 questions
28,063 answers
63,298 comments
24,173 users